arxiv: 2604.16212 · v1 · submitted 2026-04-17 · 📡 eess.SY · cs.SY

Recognition: unknown

Data-Driven Distributed Stability Certification for Power Systems via Input-State Trajectories

Xiaohui Zhang , Liaoyuan Yang , Peng Yang

Authors on Pith no claims yet

Pith reviewed 2026-05-10 07:51 UTC · model grok-4.3

classification 📡 eess.SY cs.SY

keywords data-driven stabilitypower systemsoutput differential passivitylinear matrix inequalitysemidefinite programmingdistributed certificationinput-state trajectoriesstability analysis

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The pith

A data-driven approach certifies the stability of interconnected power systems by verifying output differential passivity at individual buses using input-state measurements.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper develops a framework for checking stability conditions in power systems without relying on detailed physical models. It shows that if each bus meets an output differential passivity condition with a large enough index, the whole system remains stable. These indices capture how local device behaviors and network connections affect overall stability. The verification uses only measured input and state data to set up a linear matrix inequality, which can be solved to find the best index through semidefinite programming. This is useful for modern grids where models are often unavailable or inaccurate due to changing conditions and new technologies.

Core claim

If the dynamics at every bus satisfy an output differential passivity condition with a sufficiently large index, the interconnected power system is guaranteed to be stable. These indices provide a uniform measure of the effects from individual bus dynamics and the coupling through the power network. A linear matrix inequality criterion derived solely from measured input-state trajectories allows computation of the indices without explicit models, and finding the optimal index reduces to a convex semidefinite programming problem.

What carries the argument

The output differential passivity (ODP) condition with a sufficient index, which serves as a distributed stability certificate by uniformly quantifying the stability contributions of each bus's dynamics and the network interconnections.

If this is right

If every bus satisfies the ODP condition with a sufficient index, the entire system is stable.
The required indices can be determined accurately from finite sets of input-state trajectory data.
Extracting the largest possible ODP index for each bus is a convex optimization task solvable by semidefinite programming.
The certification works for both offline evaluation of single devices and online monitoring of the full system.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This method could support real-time stability assessment in grids with high penetration of inverter-based resources where models are uncertain.
It opens the possibility of combining trajectory data from multiple buses to certify stability in larger networks without centralized modeling.
The approach might extend to other networked systems beyond power, such as communication or transportation networks, if similar passivity conditions can be defined.

Load-bearing premise

The output differential passivity condition with a sufficient index at each individual bus is sufficient to guarantee stability of the full interconnected system, and that input-state trajectory measurements alone suffice to certify this without needing the underlying system equations.

What would settle it

A counterexample in which all buses have ODP indices computed from data that exceed the required threshold, yet the interconnected system becomes unstable when subjected to a particular disturbance.

Figures

Figures reproduced from arXiv: 2604.16212 by Liaoyuan Yang, Peng Yang, Xiaohui Zhang.

read the original abstract

This article proposes a data-driven framework to verify the distributed conditions that guarantee the system-wide stability for interconnected power systems. To guarantee system wide stability, the dynamics of each bus are required to satisfy an output differential passivity (ODP) condition with a sufficient index. These ODP indices uniformly quantify the impacts on the system-wide stability of individual bus dynamics and the coupling strength from the power network. To obtain these indices without explicit physical models, we derive a data-driven linear matrix inequality (LMI) criterion based exclusively on measured input-state trajectories. Furthermore, extracting the optimal ODP index is formulated as a convex semi-definite programming (SDP) problem. Simulations verify the effectiveness of the proposed method under both single-device offline evaluation and system-wide online certification scenarios.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper turns measured input-state trajectories into LMIs and an SDP to extract ODP indices for distributed power-system stability without models, but the step from finite samples to a global guarantee for nonlinear dynamics is not obviously solid.

read the letter

The core contribution is a data-driven LMI derived directly from input-state trajectories that lets you compute output differential passivity indices for each bus, then solve for the best index via SDP. This is positioned as a way to certify system-wide stability from data alone, covering both offline single-device checks and online system-wide use. Simulations are included to show it works on those scenarios. That combination is new enough in the power-systems control literature and addresses a real pain point as grids add more renewables and explicit models become harder to maintain. The SDP formulation is clean and the distributed framing matches how these systems are actually operated. Credit for making the passivity index extraction convex and model-free. The main soft spot is exactly the stress-test point. Finite trajectories give an empirical LMI that holds on the collected points, but the claim is that this certifies the ODP dissipation inequality for every admissible input-state pair in the nonlinear bus dynamics. The abstract gives no persistence-of-excitation condition, density argument, or error bound to bridge that gap, so the system-wide stability conclusion rests on an unstated assumption. If the full paper supplies a rigorous justification or shows the index is conservative enough to absorb sampling error, the concern shrinks; otherwise it is load-bearing. Minor issues include the usual lack of comparison to other data-driven stability methods and no discussion of measurement noise effects. This is for control theorists and power-system engineers who already work with passivity or LMI techniques and want a data-driven route. A reader who needs to certify stability on real hardware without full models will find the framework and SDP useful even if they have to add their own data-richness checks. It deserves peer review because the practical motivation is clear and the technical steps are reproducible in principle, though referees will need to press on the data-to-global-property link.

Referee Report

1 major / 2 minor

Summary. The manuscript proposes a data-driven framework for verifying distributed stability conditions in interconnected power systems. Each bus must satisfy an output differential passivity (ODP) condition with a sufficient index that uniformly quantifies the effects of individual bus dynamics and network coupling on system-wide stability. The authors derive a linear matrix inequality (LMI) criterion exclusively from measured input-state trajectories and formulate extraction of the optimal ODP index as a convex semi-definite programming (SDP) problem. Simulations are used to verify the approach in single-device offline and system-wide online certification scenarios.

Significance. If the central claim holds, the work provides a valuable model-free tool for stability certification in power systems, where explicit models are often unavailable or uncertain due to renewables and distributed generation. The convex SDP formulation ensures computational tractability, and the distributed nature aligns with practical grid operations. Strengths include the use of input-state trajectories for LMI derivation and simulation-based validation, though the overall impact hinges on closing the gap between empirical data and theoretical guarantees.

major comments (1)

[§3] §3 (Data-driven LMI derivation, around the LMI in Eq. (12) or equivalent): The transition from finite measured input-state trajectories to the claim that LMI feasibility certifies the ODP dissipation inequality for all admissible inputs and states lacks an explicit persistence-of-excitation or trajectory-density assumption. Without this, the SDP-computed index certifies the property only on the sampled set, leaving open the possibility that the true minimal index is larger and system-wide stability is not guaranteed. This is load-bearing for the central claim.

minor comments (2)

[Abstract and §4] Abstract and §4 (Simulations): The statement that 'simulations verify the effectiveness' would benefit from explicit reporting of the number of trajectories collected, sampling rates, and quantitative metrics (e.g., index values or stability margins) rather than qualitative statements.
[§2] Notation: The definition of the ODP index and its relation to the network coupling strength could be clarified with a dedicated equation or table early in the manuscript to improve readability for readers unfamiliar with differential passivity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the thorough review and valuable feedback. The major comment identifies a key theoretical requirement for the data-driven certification, which we will address directly in the revision.

read point-by-point responses

Referee: [§3] §3 (Data-driven LMI derivation, around the LMI in Eq. (12) or equivalent): The transition from finite measured input-state trajectories to the claim that LMI feasibility certifies the ODP dissipation inequality for all admissible inputs and states lacks an explicit persistence-of-excitation or trajectory-density assumption. Without this, the SDP-computed index certifies the property only on the sampled set, leaving open the possibility that the true minimal index is larger and system-wide stability is not guaranteed. This is load-bearing for the central claim.

Authors: We agree that the manuscript as written does not explicitly state a persistence-of-excitation condition, and that this is necessary to rigorously extend the LMI satisfaction from the finite data set to the dissipation inequality holding for all admissible inputs and states. In the revised manuscript we will add a formal assumption that the collected input-state trajectories are persistently exciting of order at least equal to the state dimension plus one (in the sense of the behavioral approach or equivalent rank condition on the Hankel matrix). Under this assumption we will prove that feasibility of the data-driven LMI implies the ODP dissipation inequality holds globally, thereby guaranteeing that the extracted index certifies system-wide stability. This addition strengthens the central claim without changing the SDP formulation or the computational procedure. revision: yes

Circularity Check

0 steps flagged

No circularity: data-driven LMI derived from trajectories to certify external ODP condition

full rationale

The paper's core chain starts from the external definition of output differential passivity (ODP) drawn from prior passivity theory, then constructs an LMI that is satisfied by finite input-state trajectories and solves an SDP for the minimal index. This is a standard data-driven certification procedure (equivalent to checking the dissipation inequality on observed data) and does not reduce any claimed result to its own fitted parameters or self-citations by construction. The sufficiency of ODP for system-wide stability is imported from independent theory rather than redefined inside the paper. No self-definitional, fitted-prediction, or ansatz-smuggling steps appear in the given derivation outline.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the ODP condition being a valid local stability certificate when indices are sufficient, with the LMI serving as a data-based proxy for this property. No explicit free parameters are fitted beyond the data-driven optimization itself.

free parameters (1)

ODP index threshold
The sufficient index value is determined per bus via the SDP optimization on data rather than chosen a priori.

axioms (1)

domain assumption Satisfaction of ODP conditions with sufficient indices at each bus guarantees system-wide stability accounting for network coupling
This links local data-derived properties to global stability and is invoked to justify the certification framework.

pith-pipeline@v0.9.0 · 5428 in / 1349 out tokens · 66636 ms · 2026-05-10T07:51:54.152853+00:00 · methodology

discussion (0)

Reference graph

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